Abstract: The present invention relates to a rotary machine that can be employed in different applications such as, for example, a combustion engine or compressor. The invention further relates to an assembly of two or more rotary machines and a combustion engine based on the rotary machine. The machine is substantially composed of a helical screw-shaped rotor connected to an outgoing shaft journal, which screw-shaped rotor rotates in a cylindrical housing. The machine is further provided with rotating chamber dividing bodies whose rotation is synchronised with the rotating screw-shaped rotor. The chamber dividing bodies divide the helical screw grooves into chambers whose volume varies with rotation of the screw-shaped rotor.